class_docstr: Base class for PCA methods.
  
  Warning: This class should not be used directly.
  Use derived classes instead.
class_docstr_tok: ["Base","class","for","PCA","methods",".","Warning",":","This","class","should","not","be","used","directly",".","Use","derived","classes","instead","."]
docstr: Compute data precision matrix with the generative model.
  
  Equals the inverse of the covariance but computed with
  the matrix inversion lemma for efficiency.
  
  Returns
  -------
  precision : array, shape=(n_features, n_features)
      Estimated precision of data.
docstr_tok: ["Compute","data","precision","matrix","with","the","generative","model",".","Equals","the","inverse","of","the","covariance","but","computed","with","the","matrix","inversion","lemma","for","efficiency",".","Returns","--","--","--","-","precision",":","array",",","shape=","(","n_features",",","n_features",")","Estimated","precision","of","data","."]
code: def get_precision(self):
      """Compute data precision matrix with the generative model.
  
      Equals the inverse of the covariance but computed with
      the matrix inversion lemma for efficiency.
  
      Returns
      -------
      precision : array, shape=(n_features, n_features)
          Estimated precision of data.
      """
      xp, is_array_api_compliant = get_namespace(self.components_)
  
      n_features = self.components_.shape[1]
  
      # handle corner cases first
      if self.n_components_ == 0:
          return xp.eye(n_features) / self.noise_variance_
  
      if is_array_api_compliant:
          linalg_inv = xp.linalg.inv
      else:
          linalg_inv = linalg.inv
  
      if self.noise_variance_ == 0.0:
          return linalg_inv(self.get_covariance())
  
      # Get precision using matrix inversion lemma
      components_ = self.components_
      exp_var = self.explained_variance_
      if self.whiten:
          components_ = components_ * xp.sqrt(exp_var[:, np.newaxis])
      exp_var_diff = exp_var - self.noise_variance_
      exp_var_diff = xp.where(
          exp_var > self.noise_variance_,
          exp_var_diff,
          xp.asarray(0.0, device=device(exp_var)),
      )
      precision = components_ @ components_.T / self.noise_variance_
      _add_to_diagonal(precision, 1.0 / exp_var_diff, xp)
      precision = components_.T @ linalg_inv(precision) @ components_
      precision /= -(self.noise_variance_**2)
      _add_to_diagonal(precision, 1.0 / self.noise_variance_, xp)
      return precision
  
file_path: scikit-learn/sklearn/decomposition/_base.py
imports: from abc import ABCMeta, abstractmethod
  import numpy
  from scipy import linalg
  from scipy.sparse import issparse
  from ..base import BaseEstimator, ClassNamePrefixFeaturesOutMixin, TransformerMixin
  from ..utils._array_api import _add_to_diagonal, device, get_namespace
  from ..utils.sparsefuncs import _implicit_column_offset
  from ..utils.validation import check_is_fitted
label_desc: Use image node_id 2 for calling the _BasePCA obj's underlying member method code with example usage: obj.get_precision() and returns: precision, unknown, linalg_inv